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Unformatted text preview: JOURNAL OF AIRCRAFT Vol. 38, No. 6, NovemberDecember 2001 Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models Natalia M. Alexandrov NASA Langley Research Center, Hampton, Virginia 23681-2199 Robert Michael Lewis College of William and Mary, Williamsburg, Virginia 23187-8795 and Clyde R. Gumbert, Lawrence L. Green, and Perry A. Newman NASA Langley Research Center, Hampton, Virginia 23681-2199 This work discusses an approach, rst-order approximationand model managementoptimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lower- delity, cheaper models in iterative procedures with occasional, but systematic, recourse to higher- delity, more expensive models for monitoring the progress of design optimization. A distinctive feature of the ap- proach is that it is globally convergent to a solution of the original, high- delity problem. Variants of AMMO based on three nonlinear programming algorithms are demonstrated on a three-dimensional aerodynamic wing opti- mization problem and a two-dimensionalairfoil optimizationproblem. Euler analysison meshes of varying degrees of re nement provides a suite of variable- delity models. Preliminary results indicate threefold savings in terms of high- delity analyses for the three-dimensional problem and twofold savings for the two-dimensional problem. Nomenclature C D = drag coef cient C L = lift coef cient C l = rolling moment coef cient C M = pitching moment coef cient c E = equality constraints c I = inequality constraints f = objective function M 1 = freestream Mach number S = semispan wing planform area x ; x L ; x U = design variables and bounds = angle of attack 1 = trust-region radius Introduction W E describe a general approach to design optimization, the rst-order approximation and model management optimization (AMMO) framework, that integrates engineering and Received 5 April 2000; revision received 12 June 2001; accepted for pub- lication 8 August 2001. Copyright c 2001 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Govern- mental purposes. All other rightsare reserved by the copyrightowner. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/01 $10.00 in correspondence with the CCC. Research Scientist, Multidisciplinary Optimization Branch, Aerospace Systems Concepts and Analysis, M/S 159; email@example.com....
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